Binding constant microscopic

A pyruvate concentration (mM) intrinsic or microscopic binding constant... 

There seems to be some confusion regarding adjectives appended to the various binding constants, such as macroscopic, microscopic, intrinsic, perturbed, and unperturbed. We use here a system of two different sites to clarify these concepts. For a system of two sites a and b the individual binding isotherms (BI) are... 

Thus, k is the intrinsic binding constant for the site a, while kab is the intrinsic binding constant for the pair of sites a and b. When the sites are identical, then one should take care to distinguish between the thermodynamic (sometimes referred to as macroscopic) constant Ky, which is the binding constant to the rsr site, and the intrinsic (sometimes referred to as microscopic) binding constant Ky/2, which refers to a specific single site. In the case of two different sites, the thermodynamic first constant, as measured from the total BI, is simply k + k. ... 

A smaller secondary microscopic association constant compared to the first binding constant (k, = k2 > k2, = kl2) results in anticooperative binding behavior in cases A and B. If k, = k2 < k2i = kl2, as in cases D and E, the cooperative binding yields a higher amount of higher-order complexes. 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

While Eq. 7-12, known as the Adair equation,11 might seem to provide a complete description of the binding process, it usually does not. In many cases, there is more than one kind of binding site on a macromolecule and Eq. 7-12 tells us nothing about the distribution of the ligand X among different sites in complex PX. To consider this problem we must examine the microscopic binding constants. 

The calculation procedures ascribed above have practical importance. They can be employed to predict the distribution ratio of a metal ion, DJJ, between the bulk solution phase and the ion-exchanger phase. The distribution proRles at various pH s and salt concentrations can be estimated just by use of the unique microscopic stability constant, (Pi)q, if the monodentate complex formation reaction is predominant. With dehned as the ratio of the amount of the bound metal ions to the total capacity of the carboxydate ion exchanger is related to the intrinsic binding constant, K, as shown... 

The individual microscopic binding constants cannot, however, be measured from the binding curve Only four average, macroscopic binding constants can be directly observed. This result is a result of several factors, foremost of which is the high cooperativity of O2 binding itself, which suppresses the... 

The microscopic O2 binding constants thus determined reveal a particularly strong energetic coupling between the subunits... 

Table 1 Relationship between macroscopic and microscopic O2 binding constants...

Figure 2 The dependence of O2 binding on Hb concentration. Binding curves are shown (solid black lines) for Hb concentrations of 0.005, 0.04, 0.10, 0.27,1.0, 5.4, and 38 pM (from left to right). Theoretical binding curves (broken red lines) are shown for a pure tetramer solution and a pure dimer solution. The macroscopic, thermodynamic linkage scheme relates the dimer tetramer assembly constants to the O2 binding constants for free dimer and assembled tetramer. The brackets around figurines indicate that the O2 ligand may be bound at any one of the available deoxy hemesites. Thus, the macroscopic constants are average values for multiple microscopic processes.

Microscopic binding constants and statistical effects 360 Box 7-B Sickle Cell Disease, Malaria, and... 

The reaction is facilitated by a linear template T. We will assume that this template has two independent, identical, binding sites both bind substrates with the same microscopic binding constant K, to give a binary complex S-T and a ternary complex S T S. 

Each stepwise binding constant Kj can be factored into the product of a statistical factor and the corresponding microscopic equilibrium constant K. The statistical factor is easily obtained considering that in the forward reaction there are n—j+1 empty sites available for the ligand, whereas in the reverse reaction there are j Hgands that may dissociate from the receptor. Accordingly, Eq. [39] holds ... 

C.d. spectroscopy has been used to study the interaction of tri-N-acetylchito-triose with human lysozymes at various pH values. The binding constants for the trisaccharide and diiferent microscopic protonated forms of lysozyme were estimated using the binding constants determined at various pH values and the microscopic ionization constants of the catalytic carboxylic acid groups (Glu-35 and Asp-52). Unlike hen and turkey lysozymes, all four species of human lysozyme showed similar binding with tri-N-acetylchitotriose. 

If the binding sites A and B are identical, then it follows immediately that Aia = Aib and A2A = A2b- We define this quantity as the first microscopic binding constant = Aim with Aim - Aia = Aib- Likewise, it follows that the second microscopic binding constant can be defined as = A2m with A2m = KiA = A2B- It is not possible to measure these microscopic binding constants directly but it is easy to link them to the macroscopic stepwise binding constants Ai and A2 using (52) and (53) to obtain (54) and (55). 

Alternatively, as Anderson and Hunter pointed out, the interaction parameter = a simply reflects the ratio of the microscopic binding constants Aim and A2m according... 

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